Giving up on infinite processes
There is no actual infinity, the Cantorians have forgotten that, and they have fallen into contradiction.
Henri Poincaré 1908
… classical logic was abstracted from the mathematics of finite sets and their subsets …. Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. This is the Fall and original sin of [Cantor's] set theory ….
Hermann Weyl 1946